The relational model is injective for Multiplicative Exponential Linear Logic (without weakenings)

Details The relational model is injective for Multiplicative Exponential Linear Logic (without weakenings) The relational model is injective for Multiplicative Exponential Linear Logic (without weakenings)

2010-02-16

arxiv.org/abs/1002.3131v2

Computer Science

Logic in Computer Science

36 pages

Scientific paper

We show that for Multiplicative Exponential Linear Logic (without weakenings) the syntactical equivalence relation on proofs induced by cut-elimination coincides with the semantic equivalence relation on proofs induced by the multiset based relational model: one says that the interpretation in the model (or the semantics) is injective. We actually prove a stronger result: two cut-free proofs of the full multiplicative and exponential fragment of linear logic whose interpretations coincide in the multiset based relational model are the same "up to the connections between the doors of exponential boxes".

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